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Simplifying (7m2 + -3m) + -1(6m2 + 8m + -1) = 0 Reorder the terms: (-3m + 7m2) + -1(6m2 + 8m + -1) = 0 Remove parenthesis around (-3m + 7m2) -3m + 7m2 + -1(6m2 + 8m + -1) = 0 Reorder the terms: -3m + 7m2 + -1(-1 + 8m + 6m2) = 0 -3m + 7m2 + (-1 * -1 + 8m * -1 + 6m2 * -1) = 0 -3m + 7m2 + (1 + -8m + -6m2) = 0 Reorder the terms: 1 + -3m + -8m + 7m2 + -6m2 = 0 Combine like terms: -3m + -8m = -11m 1 + -11m + 7m2 + -6m2 = 0 Combine like terms: 7m2 + -6m2 = 1m2 1 + -11m + 1m2 = 0 Solving 1 + -11m + 1m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -11m + -1 + m2 = 0 + -1 Reorder the terms: 1 + -1 + -11m + m2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -11m + m2 = 0 + -1 -11m + m2 = 0 + -1 Combine like terms: 0 + -1 = -1 -11m + m2 = -1 The m term is -11m. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11m + 30.25 + m2 = -1 + 30.25 Reorder the terms: 30.25 + -11m + m2 = -1 + 30.25 Combine like terms: -1 + 30.25 = 29.25 30.25 + -11m + m2 = 29.25 Factor a perfect square on the left side: (m + -5.5)(m + -5.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (m + -5.5) equal to 5.408326913 and -5.408326913.Subproblem 1
m + -5.5 = 5.408326913 Simplifying m + -5.5 = 5.408326913 Reorder the terms: -5.5 + m = 5.408326913 Solving -5.5 + m = 5.408326913 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + m = 5.408326913 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + m = 5.408326913 + 5.5 m = 5.408326913 + 5.5 Combine like terms: 5.408326913 + 5.5 = 10.908326913 m = 10.908326913 Simplifying m = 10.908326913Subproblem 2
m + -5.5 = -5.408326913 Simplifying m + -5.5 = -5.408326913 Reorder the terms: -5.5 + m = -5.408326913 Solving -5.5 + m = -5.408326913 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + m = -5.408326913 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + m = -5.408326913 + 5.5 m = -5.408326913 + 5.5 Combine like terms: -5.408326913 + 5.5 = 0.091673087 m = 0.091673087 Simplifying m = 0.091673087Solution
The solution to the problem is based on the solutions from the subproblems. m = {10.908326913, 0.091673087}
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